- FindStat

Identifier

St000847: Binary words ⟶ ℤ

Values

0 => 1

1 => 1

00 => 1

01 => 1

10 => 1

11 => 1

000 => 1

001 => 1

010 => 2

011 => 1

100 => 1

101 => 2

110 => 1

111 => 1

0000 => 1

0001 => 1

0010 => 2

0011 => 1

0100 => 2

0101 => 3

0110 => 2

0111 => 1

1000 => 1

1001 => 2

1010 => 3

1011 => 2

1100 => 1

1101 => 2

1110 => 1

1111 => 1

00000 => 1

00001 => 1

00010 => 2

00011 => 1

00100 => 3

00101 => 3

00110 => 2

00111 => 1

01000 => 2

01001 => 4

01010 => 6

01011 => 3

01100 => 2

01101 => 4

01110 => 2

01111 => 1

10000 => 1

10001 => 2

10010 => 4

10011 => 2

10100 => 3

10101 => 6

10110 => 4

10111 => 2

11000 => 1

11001 => 2

11010 => 3

11011 => 3

11100 => 1

11101 => 2

11110 => 1

11111 => 1

000000 => 1

000001 => 1

000010 => 2

000011 => 1

000100 => 3

000101 => 3

000110 => 2

000111 => 1

001000 => 3

001001 => 5

001010 => 7

001011 => 3

001100 => 3

001101 => 4

001110 => 2

001111 => 1

010000 => 2

010001 => 4

010010 => 8

010011 => 4

010100 => 7

010101 => 11

010110 => 7

010111 => 3

011000 => 2

011001 => 5

011010 => 7

011011 => 5

011100 => 2

011101 => 4

011110 => 2

011111 => 1

100000 => 1

100001 => 2

100010 => 4

100011 => 2

100100 => 5

100101 => 7

100110 => 5

>>> Load all 1200 entries. <<<

search for individual values

searching the database for the individual values of this statistic

/ search for generating function

searching the database for statistics with the same generating function

click to show known generating functions

Description

The number of standard Young tableaux whose descent set is the binary word.
A descent in a standard Young tableau is an entry $i$ such that $i+1$ appears in a lower row in English notation.
For example, the tableaux $[[1,2,4],[3]]$ and $[[1,2],[3,4]]$ are those with descent set $\{2\}$, corresponding to the binary word $010$.

Code

def statistic(w):
    D = [i+1 for i in range(len(w)) if w[i]==1]
    return len([T for T in StandardTableaux(len(w)+1)
                if T.standard_descents() == D])

Created

Jun 15, 2017 at 08:07 by Martin Rubey

Updated

Jun 15, 2017 at 08:07 by Martin Rubey